13 citations · 73 across the 22 of their papers we have counts for
10 papers · 1 filter
A note on the integrability of exceptional potentials via polynomial bi-homogeneous potentials
Primitivo B. Acosta-Humánez, Martha Álvarez-Ramírez, Teresinha J. Stuchi
This paper is concerned with the polynomial integrability of the two-dimensional Hamiltonian systems associated to complex homogeneous polynomial potentials of degree of type $…
Transcritical Bifurcations and Algebraic Aspects of Quadratic Multiparametric Families
Jorge Rodríguez Contreras, Alberto Reyes Linero, Bladimir Blanco Montes +1
This article reveals an analysis of the quadratic systems that hold multiparametric families therefore, in the first instance the quadratic systems are identified and classified in…
Non-integrability of the axisymmetric Bianchi IX cosmological model via Differential Galois Theory
Primitivo Acosta-Humánez, Juan J. Morales-Ruiz, Teresinha J. Stuchi
We investigate the integrability of an anisotropic universe with matter and cosmological constant formulated as Bianchi IX models. The presence of the cosmological constant causes…
Algebraic and qualitative aspects of quadratic vector fields related with classical orthogonal polynomials
Primitivo B Acosta-Humánez, Maria Campo Donado, Alberto Reyes Linero +1
This paper is a sequel of the reference \cite[§4.2, p.p. 1782--1783]{almp}, in where some families of quadratic polynomial vector fields related with orthogonal polynomials were st…
Nonintegrability of the unfoldings of codimension-two bifurcations
Primitivo B. Acosta-Humánez, Kazuyuki Yagasaki
Codimension-two bifurcations are fundamental and interesting phenomena in dynamical systems. Fold-Hopf and double-Hopf bifurcations are the most important among them. We study the…
Algebraic and qualitative remarks about the family
Primitivo B. Acosta-Humánez, Alberto Reyes-Linero, Jorge Rodríguez-Contreras
The aim of this paper is the analysis, from algebraic point of view and singularities studies, of the 5-parametric family of differential equations \begin{equation*}\label{folpz} y…
Simple permutations with order by means of Pasting and Reversing
Primitivo B. Acosta-Humánez, Oscar E. Martínez-Castiblanco
The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Humánez \& Bernhardt (power of two). It is well known that Sharkovskii's theorem…
Non-integrability Criterium for Normal Variational Equations around an integrable Subsystem and an example: The Wilbeforce spring-pendulum
Primitivo B. Acosta-Humánez, Martha Alvarez--Ramírez, David Blázquez-Sanz +1
In this paper we analyze the non-integrability of the Wilbeforce pendulum by means of Morales-Ramis theory in where is enough to prove that the Galois group of the variational equa…
On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory
Primitivo B. Acosta-Humánez, J. Tomás Lázaro-Ochoa, Juan J. Morales-Ruiz +1
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. I…
Simple permutations with order . Part I
Primitivo B. Acosta-Humánez, Eduardo Martínez Castiblanco
The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Humánez & Bernhardt (power of two). It is well known that Sharkovskii's theorem…